Control systems are widely used today for machines, devices and industrial and economic processes. A configuration for a general control system is shown in FIG. 1. The system 10 to be controlled is connected in a feedback configuration with controller 12 which attempts to drive the system output 18 to the value of reference input 14. System output 18 is fed back via feedback path 16 where it is subtracted from reference input 14 to form an error signal 22. This error signal 22 is processed by controller 12 to generate a control output 20 which is in turn fed to the input of system 10. While there are a whole host of different control configurations and structures in use today, one with ordinary skill-in-the-art will realize that FIG. 1 represents the basic building block for these controllers.
Arguably the most difficult class of systems to control are nonlinear systems. Many tools available for linear control do not apply to the control of systems which have significant nonlinearities. In these cases, more sophisticated and more complex controllers are required.
One class of control implementations is the polynomial controller. In the polynomial controller, the control output is a polynomial function of the control input. A control method using a polynomial controller was presented by Stuckman and Laursen, "A Method of Control System Design Using Global Search", IEEE Transactions on Automatic Controls, Vol. AC-34, No. 1, January 1989. Furthermore, related inventions (2), (3), and (4) present methods and systems which use polynomial controllers for controlling nonlinear systems based upon control transfer characteristic data.
While yielding effective controls, these control methods do not necessarily guarantee that their overall response will be stable. Therefore, there is a significant need for a controller which can control a nonlinear system in such a fashion that the stability of the system is guaranteed.